> ... Then, he *asked the class*> what they wanted to study. He let his students talk, with> very little coming from the teacher. After a couple of> minutes, the class (and the teacher) agreed on what they> will do. Then, the teacher calmly pulled out a sheet of> paper with the day's objective as decided by the class> preprinted and put it on the board. I think this episode> shows me that the teacher is very good at anticipating> students' thinking *and* also very skillful in facilitating> (orchestrating?) the discussion.

This description suddenly reminded me of something I observed manyyears ago in my conversations with Shizuo Kakutani, a mathematician atYale, during the year 1955-1956 when I spent a post-doctoral year there.Kakutani was a fine mathematician and always willing to spend time withstudents and people like me, and he *knew* a lot. Yet when he openedanother thread of conversation with me he always, I came to observe, beganby *asking* me something: "Do you think that...?" "Perhaps the authormeans...?" "What do you think would be different if ...?"

This was invariably a place where Kakutani wanted to *tell* mesomething, not ask my opinion. A place where he knew the answer, as heknew so many answers that I did not (then and now, too). I would offer anopinion, perhaps, or a reason, and if I was right he would think and sayhe believed so too, because ..., and I would realize that he had juststraightened me out on something. If my opinion was incorrect, he wouldask why, or raise an eyebrow and say, "But then ..." rather tentatively,as if he were exploring the territory for the first time, along with me.However it went, he ended by giving me the answer when I needed it, but,as I came to understand, without coming right out and claiming he knewsomething I did not. That would have been impolite by his standards, Isuppose.

At any rate, this was my reading of the way he spoke with me,though in some cases he really did come out and produce a theorem orreference I needed without so elaborate a preparation. And of course hedid lecture in his courses. *Telling* truths to other people cannot*always* be considered impolite. There were probably other dimensions tohis behavior in this regard than I have been able to see. I imagined atthe time that this indirect way of *telling* was something in the Japaneseculture. (Kakutani was very Japanese, and spent the war years -- my war --in Tokyo, though he had visited America before the war, and came here tolive afterwards.)

If my cultural conjecture is correct, this explains the way theteacher described by Watanabe obtained the opinion of the class that thelesson they wanted to learn that day was, mirabile dictu, exactly the onehe had prepared. But as Kakutani was the only Japanese I have ever knownmore than just in passing, it might be that I am assigning to Japaneseculture something that is actually characteristic of just that man. Itis, in any case, not a bad style for some purposes, though it takes up alittle time. However it plays out, a little intentional courtesy is a goodthing, even though its manifestation is sometimes artificial. But all artis artificial, after all, and we don't knock art for failure to benatural. "Without art, what is life?"